CHAPTER 2: THE THEORETICAL UNDERPINNINGS OF THE EQUITY
2.5 The Fisher Hypothesis
rate (Howells and Bain, 2008). Fisher’s theory essentially separates the nominal interest rate into two component parts, the real interest rate plus an expected rate of inflation, and puts forward the proposition that in a perfectly efficient economy a one-to-one relationship should exist between the inflation rate and the nominal interest rate, the difference between the two being equal to the real interest rate (Cooray, 2002).
In addition, Fisher’s theory dictates that the nominal interest rate fully reflects all available information of the possible future values of the inflation rate. Gultekin (1983a) states that the generalized Fisher Hypothesis assumes that the market is efficient and that fluctuations of the expected real return on common stock are not directly dependent on the expected inflation rate.
Ultimately this results in an aggregate compensation to investors for decreases in purchasing power caused by inflation, due to the fact that stocks are theoretically able to maintain their real value. Nelson (1976) states that in the early 70’s, prior to the empirical evidence that led to the Proxy Hypothesis, the proposition that rates of return on common stocks move directly with the rate of inflation was widely agreed upon, both in the academic and non-academic communities. The application of the Fisher Hypothesis to the equity returns-inflation relationship rests on the theory that the value of equities is inherently based on underlying assets and capital investments, which should maintain a constant real value irrespective of the rate of inflation (Bradley and Jarrell, 2008). Under this assumption of a consistent real return on capital investment, the company’s nominal cash flow derived from these investments should experience a growth rate equal to the rate of inflation (Bradley and Jarrell, 2008). Should the one-to-one relationship between the returns on an asset and inflation hold true, in accordance with the Fisher Hypothesis, then the asset in question acts as an effective hedge against inflation.
Katzur and Spierdijk (2010) state that the Fisher Hypothesis postulates that the anticipated rate of inflation is fully integrated into the ex-ante nominal interest rate while simultaneously disqualifying the existence of a relationship between the expected real interest rate and expected inflation. The idea that ex-ante nominal returns are able to integrate the expected inflation rates in the market can be applied to all assets, implying that expected nominal returns on any asset, including equities, should move on a one-to-one basis with inflation (Katzur and Spierdijk, 2010). This proposition implies a link between all capital assets and inflation, indicating that all real assets should act to some extent as an inflationary hedge when their value increases as a result of an increase in inflation. According to Alagidede and Panagiotidis
(2010), if the ex-ante real interest rate is assumed to remain constant, economic agents will require a nominal rate of return that is able to compensate for any decreases in the purchasing power of money due to inflation. In the context of stock markets, the Fisher Hypothesis implies that a positive one-to-one relationship exists between stock market returns and inflation, making stock market returns an effective inflationary hedge because the real rate of return on the stock would mitigate the loss in real wealth caused by inflation (Alagidede and Panagiotidis, 2010).
The Fisher Hypothesis predicts that the returns on common stocks when taken as an average will act as a hedge against inflation when the fluctuations in expected nominal return on common stocks are parallel to fluctuations in the expected inflation rate (Gultekin, 1983a).
Barsky (1987) describes the Fisher Hypothesis as one of the cornerstones of neoclassical monetary theory, and states that the Fisher Hypothesis essentially dictates that the nominal interest rate should experience a "point-for-point' correlation with the expected rate of inflation.
Sharpe (2000) states that the general view of financial economics is that because stocks represent a claim on a real, or “physical asset”, that the return on stocks should vary positively with the actual rate of inflation, which would make stocks an effective hedge against unexpected inflation. This is due to the fact that whenever inflation experiences an unexpected increase the nominal value of a stock would experience an equivalent increase, causing the real value of the stock to remain constant.
According to Berument and Jelassi (2002), there is a disparity in the academic community over how long a period this relationship exists for, with some authors predicting the existence of a positive relationship regardless of the time period considered, such as Boudoukh and Richardson (1993), and others, such as Mishkin (1992), who found evidence that the relationship exists exclusively in the long-run. Boudoukh and Richardson (1993) argue that the relationship still exists in the short-run, but that the Fisher effect is stronger over longer time horizons. They provide strong evidence of a positive relationship over long horizons but also state that their evidence should be consistent with certain sub-periods during the past two centuries. This debate develops into the idea that the time period considered may have an influential effect when testing for the presence of the Fisher Hypothesis within a data set.
Several studies using modern revisions of cointegration theory to test the Fisher effect have provided evidence in support of a positive relationship between inflation and nominal interest rates that is at least equal to unity. These include studies by Kim and Ryoo (2011), who provided evidence of a positive relationship greater than unity in the US, and by Alagidede and
Panagiotidis (2010) who provided evidence of a relationship between inflation rates and nominal stock returns that actually exceeds unity in South Africa. These studies, which lend support to the Fisher Hypothesis, are discussed further in chapter three.
Berument and Jelassi (2002) provide a slightly more developed form for the equation used to test the Fisher Hypothesis, which although mathematically equivalent, provides a marginally more revealing insight into the nature of the equation:
𝑖𝑡 = 𝛼 + 𝛽𝜋𝜏е
Where it represents the nominal interest rate, 𝜋𝜏е represents the expected inflation rate for the period, 𝛼 represents the real interest rate and 𝛽 is the coefficient which assumes the value of one should the Fisher Hypothesis hold.
The slight difference between this form of the model and the previous model is the addition of 𝛽 to the equation, which is expected to take on the value one, which reflects the one-to-one relationship between interest rates and the expected inflation rate, as is expected should the Fisher Hypothesis hold, a case that is referred to by Berument and Jelassi (2002) as the strong form of the Fisher Hypothesis. In its weak form 𝛽 still takes on a positive value, but this value is less than one. In the case of the strong form of the Fisher Hypothesis the 𝛽 value of one, which reflects a one-to-one relationship between nominal interest rates and the expected rate of inflation, implies that equities are able to act as a full hedge against inflation, while the weak form case of the Fisher Hypothesis implies that equities are only able to act as a partial hedge against inflation. The 𝛽 coefficient can also take on a negative value, which would mean that equities are unable to provide even a partial inflationary hedge. Alagidede and Panagiotidis (2010) state that in the case where return on equities is subject to taxes the 𝛽 coefficient would need to assume a value greater than unity for equities to be an effective hedge against inflation.
Alagidede and Panagiotidis (2010) utilise a similar model as was specified above to represent the theory of the Fisher Hypothesis, which they then develop into a regression of stock returns on contemporaneous inflation. This regression, specified below, contributes further to an understanding of the concept of the Fisher Hypothesis:
∆𝑆𝑡 = 𝛼 + 𝛽𝐸(∆𝑃𝑡|𝜑𝑡−1) + 𝜀𝑡
Where ∆𝑆𝑡 represents the nominal stock return, ∆𝑃𝑡 represents the inflation rate, 𝛼 represents the expected real rate of stock return, 𝛽 is the coefficient which assumes the value of one should
the Fisher Hypothesis hold and 𝐸(∆𝑃𝑡|𝜑𝑡−1) in the model represents inflationary expectations at time 𝑡 − 1 based on all available information, given by 𝜑𝑡−1.
The variable 𝜑𝑡−1, which represents all available information, would be subject to significant variation based on data availability and as such the variable is removed from the equation when it is run after which the equation is based on a regression of observable data. As was the case in the earlier equation, a regression that yields a 𝛽 coefficient value of one suggests that equities are able to act as a hedge against inflation, while a 𝛽 coefficient of less than one suggests that equities are unable to provide a full inflationary hedge. Of course, as stated by Alagidede and Panagiotidis (2010) the 𝛽 coefficient is able to exceed unity to satisfy the case where equity returns are subject to taxes and would therefore be required to exceed the rate of inflation by the equivalent of the tax rate in order to provide a full inflationary hedge. This is consistent with the tax-augmented Fisher Hypothesis, which is the idea that the return on stocks must be in excess of the inflation rate instead of simply equal to it, in order to compensate for the loss in real wealth of tax-paying investors. To rephrase, a finding of above-unity elasticity as indicated by a positive 𝛽 coefficient greater than one would be consistent with the tax- augmented Fisher Hypothesis (Luintel and Paudyal, 2006).
According to Khil and Lee (2000) it was commonly thought, up until the mid-1970’s, that Fisher’s theory should hold and that stock returns and inflation should be positively related, causing nominal asset returns to be closely correlated with expected inflation. Stocks’ values are based on a specific underlying asset and are therefore expected to have consistent real returns based on Fisher’s theoretical prediction that the real interest rate is unaffected by expected inflation (Khil and Lee, 2000). Note that the nominal asset returns should therefore, in theory, be positively correlated with changes in the expected inflation rate. For example, in the case of stock markets, an X percentage increase in inflation should be followed by an X percentage increase in stock returns, allowing stocks to be used as a perfect hedge against inflation (Alagidede and Panagiotidis, 2010). However, as pointed out by Barsky (1987) there was virtually no evidence of the Fisher effect in data sets taken from the United States and Britain prior to 1939. Barsky (1987) compares the relationship between the US three-month commercial paper rate with the ex-post inflation rate between 1860 and 1939 and discovers that it is negatively correlated, with a figure of -0.17. The lack of empirical evidence of a positive relationship between inflation and common stock returns in the US prior to the development
of the Fisher Hypothesis casts into question the validity of the theoretical underpinnings on which the hypothesis is based.
This being said however, recent empirical studies have provided new evidence of the existence of a positive relationship between the rate of inflation and the nominal interest rate (Alagidede and Panagiotidis, 2010; Kim and Ryoo, 2011; Eita, 2012). This evidence leads to the question of whether less modern modelling techniques have been able to incorporate the requisite factors needed to provide an accurate assessment of the relationship and whether historical results have been consistent with modern techniques for modelling the relationship. The next section introduces what is possibly the most famous counter argument to the Fisher Hypothesis, before the modern empirical evidence and modelling techniques are discussed in chapter three.